formulating the hypothesis null hypothesis 4 the null hypothesis is a statement about the population...
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Formulating the Formulating the HypothesisHypothesis
The null hypothesisnull hypothesis is a statement about the population value that will be tested. The null hypothesisnull hypothesis will be rejected only if the sample data provide substantial contradictory evidence.
Formulating the Formulating the HypothesisHypothesis
The alternativealternative hypothesis hypothesis is the hypothesis that includes all population values not covered by the null hypothesis. The alternative hypothesisalternative hypothesis is deemed to be true if the null hypothesis is rejected.
Formulating the Formulating the HypothesisHypothesis
The research hypothesis research hypothesis (usually the alternative alternative hypothesishypothesis):Decision maker attempts to demonstrate it to be true. Deemed to be the most important to the decision maker. Not declared true unless the sample data strongly indicates that it is true.
Types of Statistical ErrorsTypes of Statistical Errors
Type I ErrorType I Error - This type of statistical error occurs when the null hypothesis is true and is rejected.
Type II ErrorType II Error - This type of statistical error occurs when the null hypothesis is false and is not rejected.
Types of Statistical ErrorsTypes of Statistical Errors
State of Nature
DecisionConclude Null True(Don’t reject H00)
Null Hypothesis True Null Hypothesis False
Correct Decision Type II Error
Conclude Null False(Reject H00)
Type I Error Correct decision
Establishing the Establishing the Decision RuleDecision Rule
The critical valuecritical value isDetermined by the significance level. The cutoff value for a test statistic that leads to either rejecting or not rejecting the null hypothesis.
Establishing the Establishing the Decision RuleDecision Rule
The significance levelsignificance level is the maximum probability of committing a Type I statistical error. The probability is denoted by the symbol .
Reject H0xx25
Do not reject H0
Sampling DistributionSampling Distribution
Maximum probability of committing a Type I error =
Establishing the Establishing the Decision RuleDecision Rule
(Figure 8-3)(Figure 8-3)
z25
Rejection region = 0.10
28.1z0
From the standard normal table
28.110.0 zThen
28.1z
0.5 0.4
Establishing the Critical Establishing the Critical Value as a Value as a z z -Value-Value
Establishing the Establishing the Decision RuleDecision Rule
The test statistictest statistic is a function of the sampled observations that provides a basis for testing a statistical hypothesis.
z
Rejection region = 0.10
28.1z0
0.5 0.4
Test Statistic in the Test Statistic in the Rejection RegionRejection Region
69.2z
Establishing the Establishing the Decision RuleDecision Rule
The p-valuep-value isThe probability of obtaining a test statistic at least as extreme as the test statistic we calculated from the sample. Also known as the observed significance level.
z
Rejection region = 0.10
28.1z0
0.5 0.4
Relationship Between the p-Relationship Between the p-Value and the Rejection Value and the Rejection
RegionRegion
69.2z
p-value = 0.0036
Using the p-Value to Using the p-Value to Conduct the Hypothesis Conduct the Hypothesis
TestTest If the p-value is less than or equal p-value is less than or equal
to ato a, reject the null hypothesis. If the p-value is greater than ap-value is greater than a, do
not reject the null hypothesis.Example:For = 0.05 with the p-value = 0.02
for a particular test, then the null hypothesis is rejected.
One-Tailed Hypothesis One-Tailed Hypothesis TestsTests
A one-tailed hypothesis one-tailed hypothesis testtest is a test in which the entire rejection region is located in one tail of the test statistic’s distribution.
Two-Tailed Hypothesis Two-Tailed Hypothesis TestsTests
A two-tailed hypothesis two-tailed hypothesis testtest is a test in which the rejection region is split between the two tails of the test statistic’s distribution.
z645.1z0
Two-Tailed Hypothesis Two-Tailed Hypothesis Tests Tests
(Figure 8-7)(Figure 8-7)
645.1z
05.02
05.02
When When Is Unknown Is Unknown The sample standard deviation
is used. The test statistic is calculated as
The critical value is found from the t-table (Appendix F) using n-1 degrees of freedom.
t xs n